The Hammers fell behind inside seven minutes on the south coast and, despite Javier Hernandez equalising for the visitors, they were left behind in the second half by the clinical Seagulls.
"We didn't play well", Moyes told Sky Sports.
Though West Ham have recently issued a statement defending themselves against racism accusations, former player Diafra Sakho has said that the club doesn't want black players there. But from the corner we clear it, and to be fair, the boy (Izquierdo) scores a worldie.
When asked about Cresswell's tackle on Knockaert, Brighton manager Chris Hughton said: "I've seen [it]". But we were never really in the game today. An unchanged lineup from the 1-1 quality draw against Crystal Palace is named by Moyes, with Joao Mario hoping to build off a promising debut.More news: Pentagon Chief: No Evidence of Recent Sarin Gas Use by Syria
"What I know is we have is a huge amount of competition at this end of the table and whoever is playing each other at this end of the table it's a bigger game but we have no targets". We have got to keep looking forward to the next game, though, and try to get the points in that.
"They lie to people, they pretend I am bad because I have character", the Senegalese worldwide said on his Snapchat account. However Pascal Gross' 75th minute strike gave them a two-goal cushion heading into the closing stages of the game - the first time they had led by more than one goal since they beat the Hammers 3-0 away from home last October.
"The significance of the result at Southampton is if you are able to get a win or draw, it's points they don't get and that would apply to any team around us and West Ham fall into that category".
"You win one and lose the next week, and you're right back in it. Then, in the summer, we will see".